Who is in charge of putting together a development team?

How to make sure the development team has all the competencies they need to work to develop a product optimally?

Look at the Definition of Done. Can the team meet it?

Since we don't have lead developer, who would ask for example for QA role or senior programmer or junior or tester or DBA, information security role, technical support, business analyst or some kind of other IT specialists?

The Development Team has a responsibility to assure Done, and the development organization may have an interest. The Scrum Guide says: "If the definition of "Done" for an increment is part of the conventions, standards or guidelines of the development organization, all Scrum Teams must follow it as a minimum."

I'd suggest that if a new skill is required on the team for Done to be achieved, the party to take action on the matter should be the one which first recognizes the shortcoming.

take action on the matter should be the one which first recognizes the shortcoming.

This I like.

Anyway, there are multiple ways to approach this, but ultimately the team as a collective should be able to deliver a "Done" piece of work. This means that, like Ian pointed out, there should be a Definition of what we see as Done. Based on that you can have people volunteer, approach people directly to ask them, etc. etc. But in charge asserts there is a team leader, which I can highly recommend to avoid. In the beginning it will be the PO as he will probably be the only one on the team, if a Scrum Master joins him, they're both responsible and so on. 

I honestly have never thought to answer that question in relation to the Definition of Done.  That is one of the best answers I have ever read!  Thanks @Ian Mitchell for that one.  

The usual answer I see and give is ... 

If the Development Team feels that they need anything that they can not provide they should be the ones to ask.  After all, the Development Team is responsible for delivering the technical solutions and they will be the only ones to know if there are needs beyond what they can currently provide. The organization should empower the entire team to act on any need.  That way any one of the members can be the one that "submits the formal request" and can work with other teams to determine where a resource can be acquired.  If they need help the Scrum Master is there to help remove impediments.